Voir la notice de l'article provenant de la source Numdam
We prove sharp Hölder continuity and an estimate of rupture sets for sequences of solutions of the following nonlinear problem with negative exponent
@article{AIHPC_2016__33_1_221_0, author = {D\'avila, Juan and Wang, Kelei and Wei, Juncheng}, title = {Qualitative analysis of rupture solutions for a {MEMS} problem}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {221--242}, publisher = {Elsevier}, volume = {33}, number = {1}, year = {2016}, doi = {10.1016/j.anihpc.2014.09.009}, mrnumber = {3436432}, zbl = {1350.35093}, language = {en}, url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2014.09.009/} }
TY - JOUR AU - Dávila, Juan AU - Wang, Kelei AU - Wei, Juncheng TI - Qualitative analysis of rupture solutions for a MEMS problem JO - Annales de l'I.H.P. Analyse non linéaire PY - 2016 SP - 221 EP - 242 VL - 33 IS - 1 PB - Elsevier UR - http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2014.09.009/ DO - 10.1016/j.anihpc.2014.09.009 LA - en ID - AIHPC_2016__33_1_221_0 ER -
%0 Journal Article %A Dávila, Juan %A Wang, Kelei %A Wei, Juncheng %T Qualitative analysis of rupture solutions for a MEMS problem %J Annales de l'I.H.P. Analyse non linéaire %D 2016 %P 221-242 %V 33 %N 1 %I Elsevier %U http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2014.09.009/ %R 10.1016/j.anihpc.2014.09.009 %G en %F AIHPC_2016__33_1_221_0
Dávila, Juan; Wang, Kelei; Wei, Juncheng. Qualitative analysis of rupture solutions for a MEMS problem. Annales de l'I.H.P. Analyse non linéaire, Tome 33 (2016) no. 1, pp. 221-242. doi : 10.1016/j.anihpc.2014.09.009. http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2014.09.009/
[1] On the singular set of stationary harmonic maps, Manuscr. Math., Volume 78 (1993) no. 4, pp. 417–443 | MR | Zbl
[2] The obstacle problem revisited, J. Fourier Anal. Appl., Volume 4 (1998) no. 4–5, pp. 383–402 | MR | Zbl
[3] Singularly perturbed elliptic systems and multi-valued harmonic functions with free boundaries, J. Am. Math. Soc., Volume 21 (2008), pp. 847–862 | MR | Zbl | DOI
[4] Hausdorff dimension of ruptures sets and removable singularities, C. R. Math. Acad. Sci. Paris, Volume 346 (2008) no. 1–2, pp. 27–32 | MR | Zbl
[5] Elliptic equations with vertical asymptotes in the nonlinear term, J. Anal. Math., Volume 98 (2006), pp. 349–396 | MR | Zbl | DOI
[6] Compactness along the branch of semistable and unstable solutions for an elliptic problem with a singular nonlinearity, Commun. Pure Appl. Math., Volume 60 (2007), pp. 1731–1768 | MR | Zbl | DOI
[7] Mathematical Analysis of Partial Differential Equations Modeling Electrostatic MEMS, Courant Lect. Notes Math., vol. 20, Courant Institute of Mathematical Sciences/American Mathematical Society, New York/Providence, RI, 2010 | MR | Zbl | DOI
[8] Partial regularity for stationary harmonic maps into spheres, Arch. Ration. Mech. Anal., Volume 116 (1991) no. 2, pp. 101–113 | MR | Zbl | DOI
[9] Monotonicity properties of variational integrals, weights and unique continuation, Indiana Univ. Math. J., Volume 35 (1986) no. 2, pp. 245–268 | MR | Zbl | DOI
[10] Minimal Surfaces and Functions of Bounded Variation, Springer Monogr. Math., vol. 80, Birkhäuser, 1984 | MR | Zbl
[11] Hausdorff dimension of ruptures for solutions of a semilinear elliptic equation with singular nonlinearity, Manuscr. Math., Volume 120 (2006) no. 2, pp. 193–209 | MR | Zbl
[12] Asymptotic behavior of touch-down solutions and global bifurcations for an elliptic problem with a singular nonlinearity, Commun. Pure Appl. Anal., Volume 7 (2008) no. 4, pp. 765–786 | MR | Zbl
[13] Zero set of Sobolev functions with negative power of integrability, Chin. Ann. Math., Ser. B, Volume 25 (2004) no. 1, pp. 65–72 | MR | Zbl | DOI
[14] Properties of positive solutions to an elliptic equation with negative exponent, J. Funct. Anal., Volume 254 (2008) no. 4, pp. 1058–1087 | MR | Zbl
[15] Uniform Hölder bounds for nonlinear Schrödinger systems with strong competition, Commun. Pure Appl. Math., Volume 63 (2010) no. 3, pp. 267–302 | MR | Zbl | DOI
[16] Partial regularity for weak solutions of a nonlinear elliptic equation, Manuscr. Math., Volume 79 (1993) no. 2, pp. 161–172 | MR | Zbl
[17] A minimization problem and the regularity of solutions in the presence of a free boundary, Indiana Univ. Math. J., Volume 32 (1983) no. 1, pp. 1–17 | MR | Zbl | DOI
[18] Modeling MEMS and NEMS, Chapman & Hall/CRC, Boca Raton, FL, 2003 | MR | Zbl
[19] Some global results for nonlinear eigenvalue problems, J. Funct. Anal., Volume 7 (1971), pp. 487–513 | MR | Zbl | DOI
[20] Lectures on Geometric Measure Theory, Proceedings of the Centre for Mathematical Analysis, Australian National University, vol. 3, Australian National University, Centre for Mathematical Analysis, Canberra, 1983 | MR | Zbl
Cité par Sources :